Coin Toss and Level crossing problem

 

OBJECTIVE

• To understand and explore random process simulation

 

LEARNING OUTCOMES

• After the completion of this experiment students will be able to Simulate random processes and their statistics
•  

SOFTWARE USED:

                 MATLAB^® R2017a

1. Simulate a coin toss that maps a head as 1 and tail as 0.

2. Toss the coin N = 100, 500,1000, 5000 and 500000 times and compute the probability (p) of head in each case.

3. Compute the absolute error |0.5 − p| in each case and plot against N and understand the law of large numbers.

4. Create a uniform random vector with maximum magnitude 10, plot and observe.

5. Set a threshold (VT = 2) and count how many times the random function has crossed VT .

6. Count how many times the function has gone above and below the threshold.

PROGRAM 

clc;

clear all;

close all;

n=[10 100 500 1000 5000 10000 500000];

 

for i=1:7

    heads=0;

    tail=0;

    disp('value of n is')

    disp(n(i))

for cointoss=1:n(i)

 flip=int32(randi([0, 1]));

 if flip==1

     toss_result(cointoss)=flip;

     heads=heads+1;

 else

     toss_result(cointoss)=flip;

     tail=tail+1;

 end

end

 

disp('no. of heads is')

disp(heads);

disp('no. of tail is')

disp(tail);

disp('probability of heads is')

Prob_H=heads/n(i)

disp('probability of tail is')

Prob_T=tail/n(i)

ab_err(i) = abs(0.5 - Prob_H);

disp('absolute error')

disp(ab_err(i))

end

 

plot(n,ab_err,'linewidth',2);

title('Absolute error Vs N')

xlabel('n')

ylabel('ab_err')

OUTPUT

 

PROGRAM

clc;

clear all;

close all;

r=randi(10,[1,100]);

plot(r,'linewidth',2)

hold on;

T=2;      %threshold

for i=1:100

Threshold(i)=T;

end

plot(Threshold,'linewidth',2);

hold on;

disp('Number of values crossed threshold')

sum(r>=T)

disp('Number of values under threshold')

sum(r<T)

OUTPUT